Wilson, 68, who had served almost four months in home detention at his sister's home, was allowed to watch the judge hand down his decision via video link from a remote location so he didn't have to face the media.

The judge today also threw out an appeal by the NSW Director of Public Prosecutions against the leniency of magistrate Robert Stone's decision that Wilson should serve 12 months of home detention.

Philip Wilson has won his appeal against his conviction for concealing child sex abuse. (AAP)

The prosecution case was that Wilson was told by two altar boys in 1976 that they'd been abused by pedophile priest James Fletcher but the clergyman did nothing about it.

It was alleged he subsequently failed to go to the police after Fletcher was arrested in 2004 for abusing another boy.

One of the two altar boys, Peter Creigh, was in tears after the judge's decision today. He was too upset to comment outside court.

As the judge left the bench one onlooker called out: "Bulls---, that's a disgrace."

Wilson was facing a maximum of two years in jail when he was sentenced on August 14 to spend at least six months at his sister's home before being eligible for parole.

He was forced to resign as archbishop of Adelaide in July after becoming the most senior Catholic clergyman in the world to be convicted of covering up child sex abuse.

The magistrate who found Wilson guilty rejected claims the clergyman - who is suffering from the early stages of Alzheimer's disease - could not remember the two altar boys telling him about the abuse in 1976.

Peter Creigh, who was abused by Fletcher, broke down as the appeal was upheld. (AAP)

Fletcher was convicted in 2004 of sexually abusing another boy and died of a stroke in jail in early 2006.

The defence claimed Wilson was not guilty because the case was circumstantial and there was no evidence to prove beyond a reasonable doubt the clergyman was told about the abuse, believed it was true or remembered being told about it.

During Wilson's two-day appeal last week, prosecutor Helen Roberts urged Judge Ellis to consider how the magistrate had the benefit of watching both Wilson and Creigh - the main witness - during the trial and he'd raised doubts about the clergyman's credibility before finding him guilty.

Mr Stone found Creigh had been a genuine and truthful witness who had no motive to make up the conversation he said he had with Wilson in 1976.

But Judge Ellis repeatedly stated during the appeal that Wilson was an intelligent, articulate man who appeared to be doing his best to answer questions put to him during the trial.

He said he wasn't bound by the magistrate's conclusion that many of Wilson's answers were ''dissembling and contrived''.

When sentencing Wilson to home detention, Mr Stone said the clergyman had shown no remorse or contrition for the cover-up and his primary motive had been to protect the Catholic Church.